We report the design of the beam-transport system (especially the vertical geometry) for a cold-neutron disk-chopper spectrometer AMATERAS at J-PARC. Based on the elliptical shape, which is one of the most effective geometries for a ballistic mirror, the design was optimized to obtain, at the sample position, a neutron beam with high flux without serious degrading in divergence and spacial homogeneity within the boundary conditions required from actual spectrometer construction. The optimum focal point was examined. An ideal elliptical shape was modified to reduce its height without serious loss of transmission. The final result was adapted to the construction requirements of AMATERAS. Although the ideas studied in this paper are considered for the AMATERAS case, they can be useful also to other spectrometers in similar situations.

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